Respuesta :
Answer: The world's population in 2015 would have been 7.333 billion.
Step-by-step explanation:
- Since the increase in population is an exponential one. It then follows a geometric progression defined by, [tex]T_{n}[/tex] = [tex]ar^{n - 1}[/tex]
- Where [tex]T_{n}[/tex] is the nth term, a is the 1st term, r is the common ratio.
- Therefore, the population in 1998 is the first term a = 5.937 billion. The population in 2014 corresponds to the 17th term (i.e., n = 17) = 7.238 billion.
Hence, [tex]T_{n}[/tex] = [tex]ar^{n - 1}[/tex]
7.238 billion = 5.937 billion × [tex]r^{17 - 1}[/tex]
[tex]r^{16}[/tex] = (7.238 billion) ÷ (5.937 billion)
= 1.219
r = [tex]\sqrt[16]{1.219}[/tex]
r = 1.0125
To get the population in 2015, which is the 18th term. We use
[tex]T_{n}[/tex] = [tex]ar^{n - 1}[/tex]
[tex]T_{18}[/tex] = 5.937 billion × [tex]1.0125^{18 - 1}[/tex]
= 5.937 billion × [tex]1.0125^{17}[/tex]
= 5.937 billion × 1.235
[tex]T_{18}[/tex] = 7.333 billion
Answer:
The world's population at 2015 is 7.328 billion
Step-by-step explanation:
An exponential increase in population can be represented by the equation below:
F = p(1+r)ᵗ .....1
Where;
F = final population after time t
p = initial population
r = rate of increase in population per time
t = time
Given;
F = 7.238 billion
p = 5.937 billion
t = 2014 - 1998 = 16 years
To determine the value of r from equation 1, making r the subject of formula.
1+r = (F/p)^(1/t)
r = (F/p)^(1/t) - 1
Substituting the given values.
r = (7.238/5.937)^(1/16) - 1
r = 1.01246 - 1
r = 0.01246
Therefore, the population in 2015 can be calculated using the equation 1.
t = 2015 - 1998 = 17
p = 5.937 billion
r = 0.01246
Substituting the values into equation 1.
F(2015) = 5.937(1+0.01246)^17
F(2015) = 7.328 billion.
So, the population at 2015 is 7.328 billion.
